Fast DOA estimation based on a split subspace decomposition on the array covariance matrix

A novel real-valued root multiple signal classification (RV-root-MUSIC) algorithm for estimating the direction-of-arrival (DOA) of multiple narrow-band signals is presented. Compared with the conventional root-MUSIC with a complex subspace decomposition on the entire array covariance matrix (ACM), RV-root-MUSIC exploited a split subspace decomposition on either the real-part of ACM (R-ACM) or the imaginary-part of ACM (I-ACM) with real-valued computations. Unlike the unitary root-MUSIC (U-root-MUSIC) with exploitations on the centro-Hermitian property of ACM, the proposed method developed a new result showing that R-ACM shares the same null subspace with I-ACM, which collides with the intersection of the original noise subspace and its conjugate one. Thanks to the real coefficients, the roots of RV-root-MUSIC appear in conjugate pairs, which allows fast rooting with only real-valued computations. Therefore, both subspace decomposition and polynomial rooting can be implemented with real-valued computations, which hence results in a significant reduction in computational cost as compared to root-MUSIC and U-root-MUSIC. Simulations are conducted to verify the effectiveness of the new technique.